More sinuous than the serpent atop King Tut's golden mask and semming sometimes as endless as the mighty Nile, those daily lines of visitors to the "Treasures of Tutankhamun" at the National Gallery hav become a legend in themselves.

Since March 1, Gallery officials have extended the exhibit's hours to 8:30 every evening to let more people in. But with only a week left before the exhibit must close next Tuesday night, lines were getting longer than eve, and total attendance was drawing closer to the record 964,970 that saw the Berlin Museum paintings in 1948 and the 875,173 who viewed the Art Treasures of Vienna in 1949.

Some frustrated visitors complained that the exhibit should be kept open even later.Gallery officials said limitations on budget, and particularly on staff, made that impossible. They said that the existing staff of guards, telephone operators, checkroom attendants, salespeople (for catalogues, postcards and jewelry reproductions) and others already was stretched to the limit.

Hiring additional guards would entrail complex security checks and special training, the official added - and there just was not time for that even if qualified applicants could be found. They pointed out that National Gallery guards were responsible for security of the priceless permanent collection as well as King Tut's treasures.

Galley officials said they had anticipated before the exhibit opened that it would draw large crowds, but the current crush has far surpassed what they were expecting as recently as January.

What explains the allure of an exhibit of only 55 objects that has drawn, since opening last Nov. 17, more than 750,000 people of all ages from Anacostia and Annandale and Allentown, Pa - surpasing the entire population of the District of Columbia? People who wait in line as long as six hours or more 3/8 Who return to endure the lines a second or even third time if they don't get in at first?

"It's like you climb Mt. Everest.'It's there,' and so the exhibit is here so you have to come and see it," explained Mrs. Gerl Markoff of Silver Spring after viewing the "Treasures" one recent weekday evening.

"I think it's just that it's sort of the 'in' thing to do - 'I've been to see Tut,'" said Mrs. Robert Edmiston, down for the day from Harrisburg, Pa., with two friends, as she rested her feet afterward. "And I just can't believe that all those people in line today, especially some of those with those little tiny children, are really interested in Egyptians."

But others, who had braved the lines to pass among the ivory-inlaid chairs and lapis-encrusted jewelry, insisted they were really interested.

"I like to look at treasures," said Caryn Allen, a junior at Woodson Senior High School here who had come with her Latin class.

Older people have been drawn by their rekindled memories of news accounts more than half a century ago of the discovery of King Tut's tomb and its awesome contends. For Grace Peck of Arlington, "That was what was important."

A gaggle of fifth and sixth graders on a field trip from Lafayette School in the District had their appetites whetted through studying ancient Egypt in class though one omplained that the exhibit was "gyppy because they didn't have all the good things in it."

Gallery officials said "bus after bus" crammed with youngsters from Pennsylvania and other Northern states showed up earlier in the winter when the energy crisis forced mass school closings.

Said Sally Shelton, a foreign policy aide to Sen. Lloyd Bentsen (D-Tex.), "I was in Egypt a couple months ago, in the Valley of the Kings, and went down into King Tut's tomb - and there wasn't anything there because it was all in the United States. So I simply had to come."

J. Carter Brown, National Gallery of Art director, saw the attraction as a combination of factors: the "sheer visual seduction" and "breathtaking antiquity" of the 3,300-year-old artifacts, the "treasure-hunt quality" of their discovery, and "the spooky quality . . . the voyeurism" of viewing things never intended for 20th century mortals' eyes.

"Finally," Brown added, "there is the aspect of death, which grips us somewhere that's very, very deep." The ancient Egyptians' belief in an afterlife, their "challenge to mortality," is "something we share empathetically with all those people."

The National Gallery has publicized the exhibit, and television, magazines and newspapers have given it generous attention. But increasinly, news of its appeal has been carried by word-of-mouth.

"Just everybody's reaction," said Bill Thomas of Springfield, Va., prompted him to take time off from his Veterans Administration job to see the "Treasures."

Katherine Warwick, gallery spokeswoman, said as few as one-third of the people arriving on any given day may actually see King Tut's treasures. Many stand in line for a while, then give up. Others, seeing the lines as they approach, don't even try.

Yet the very length of the lines has been drawing people to the exhibit.

"We'd been reading about how the lines were forming," said Paul Briddell, a lie insurance agent from Salisbury, Md., "and thought, 'My God, it must be really fantastic.'" He said the lines "created a lot more excitement, you know - 'I better see this.'"

Briddell and his family had finally seen the exhibit on their third trip across the Bay from Salisbury, having left home at 4:30 that morning. It was worth it, he said: "I was highly elated."

Judith Johnson, a Bethesda anthropologist who spent 5 1/2 hours in line Feb. 25, was inspired to write about her "King Tut Marathon" experience with seven line-mates: "Strangers all, shuffling along, legs and feet aching, bodies exhausted, hypnotized and numb with fatigue and boredom - we melded together."

She continued, "We began by exchanging basic information on each other and by the end of 5 1/2 hours, we knew the most intimate details of each other's lives.

"We organized ourselves like a self-contained cell. One was sent off to reconnoiter the line ahead; another, burdened down with eight coats, to locate a cloakroom. Another was sent to check out the lunchroom.

"A fourth was discovered to be an amaetur art historian and he went off to choose a selection of art for the tours he gave the rest of us, two-by-two, in the hours to come. We took turns posing for a fifth Marathonmate, who got great practice sketching our unusual positions.

"One of our groupwas an elderly woman whom we were all concerned over. We commandered a chair for her and took turns staying with her until the line moved 25 yards. Then we'd fitnesse another chair for her and escort her there . . . "

Johnson concluded, "The exhibit was not worth the 5 1/2 hours - but the Marathon was."

Attendance will doubtless pass 800,000 before the exhibit closes Tuesday, March 15 so the treasures can move on to Chicago, second of the tour's six cities.

With fewer than 10 days remaining before King Tut's tent is struck, Gallery officials and already-weary guards were bracing for heavier crowds - including those who put off earlier visits hoping lines would dwindle.

"I tried to warn people at the beginning to come early," said Brown ruefully.

About 7 a.m. each morning, three hours before the exhibit opens to the public, the Gallery has begun handing out 1,000 tickets (two to a customer) letting recipients enter the exhibit at a specified time later in the day without waiting in line. But these tickets frequently are snapped up within an - hour.

Sunday morning, according to at least one frustrated visitor to the museum, the tickets ran out long before getting to the 500th person on line.

"We were in range," said Arthur Cree, a retired church business administrator who came from Hendersonville, N.C., to Washington to see Tut. "We were between 320 and 330 on line but we missed getting tickets by about six or eight people.

"One hundred and 50 people behind us had expected to get tickets," said Cree, who said he and others had counted to check their place in line," and they made very loud protests . . . Seven or eight police cars showed up an that helped quiet people."

It wasnot the first day on line for Cree, who said he lined up Sunday at 4:30 a.m. Saturday morning, he said, he lined up at 5:30.

Cree said he, his wife and another couple drove to Washington from their home "500 miles down the road" just to see Tut. "I remember when it was discovered in 1923," said Cree, 67. "I've read about it for the past year and I did want to see it."

Yesterday afternoon, $150 poorer, Arthur Cree, his wife and friends headed home. "We will have spent four nights on the road, two nights here and we're going back without seeing anything of it," he said.